I'm trying to work through this prob but not getting anywhere. Also can't find any example in my text or on line. I don't want to give up, can someone explain where to start? OK I'm supposed to put this matrix into echelon form:
r1- 1 a b+c
r2- 1 b a+c
r3- 1 c b+a
Just to clarify, do you need row echelon form, or reduced row echelon form?
Did your professor not explain the "rules" for manipulating matrices to get echelon form? The rules are to use elementary row operations, of which there are three, (1) switch rows, (2) multiply a row by a nonzero constant, (3) add a multiple of one row to another row. These are called row switching, row multiplication, and row addition, respectively, and a more formal treatment is given here.
I did r1-r2=r2 = 0 a-c c-a
r1-r3=r3 = 0 a-b b-a
then I multiplied r2 times 1/(a-c) and r3 times 1/(a-b)
so now my matrix looks like this: 1 a (b+c)
0 1 -1
0 1 -1
then I subtracted r3-r2= r3 = 0 0 0 and there I have my echelon form correct? now the next question in my book says find the determinant. But since I have a whole row of zeros doestn't that mean that the determinant is zero?